Yes. There are two different things going on. The first change that happens to d in some circumstances (that we call lenition), to the closely related sound /ð/ (as in there in English), is not a big deal in the sense that the sound change is not that big. This is still found as the lenited d in Cornish and (spelt dd) in Welsh.
But a second thing happened in Gaelic and Irish. This sound changed, bizarrely and for an unknown reason, to /ɣ/, just like a Gaelic gh. This has no equivalent in English. The nearest is g (as you say) but you have to let the air leak out in the same way that a th is a d or t with the air leaking out.